# How to multiply square roots?

Square is a number obtained when a number is raised to the power of two. The square roots are the inverse of squares. They are obtained by raising a number to the power of 1/2.

## Answer: To multiply square roots, we multiply the whole number part and the square root parts separately.

Let's understand the solution in detail.

**Explanation:**

Let's understand this with some examples:

**Example 1: **Multiply √15 by √11.

In this case, both of them are under the square root sign. Hence, we can multiply them directly.

⇒ √15 × √11 = √165

**Example 2: **Multiply √3 by 4.

In this case, one of them is under the square root sign and the other is a whole number. Hence, we can multiply them directly.

⇒ √3 × 4 = 4√3

Alternatively,

In this case, first, we convert 4 in such a way that it's under the square root sign.

Here, 4 = √16.

Now, we multiply them.

⇒ √3 × √16 = √48 = 4√3

Note that we could directly write it as 4√3, but it's always better to follow every step while learning.

**Example 3: **Multiply 3√5 by 3√6.

Here, first, we convert 3√5 and 3√6 to suitable forms.

Hence, 3√5 = √(5 × 9) = √45.

And 3√6 = √(6 × 9) = √54.

Now, multiplying both the numbers under the square root, we get √2430.

We can write √2430 = 9√30.

Another method is to multiply the whole number part and the radix part separately to give the answer. It is a lot easier way.

Note that we could also simply multiply as 3√5 × 3√6 = 9√30.